Fractions and Ratios
Think of a fraction as representing a part of a whole. Is there any more to it than that?
Fraction - A way of (a) representing a part of a whole or unit, (b) representing a point on a line, (c) representing a proportion of a set, (d) modelling a division problem, or (e) expressing a ratio.
Symbols - The mathematical notation used for a fraction might, in fact, be used in at least five different ways:
● to represent a proportion of a whole or of a unit;
● to represent a point on a line;
● to represent a proportion of a set;
● to model a division problem;
● as a ratio.
Ask children to discuss at home with members of their family whether they can think of any situations where they actually use fractions. Share with the rest of the class any examples that they come up with. There may not be many examples other than halves and quarters (particularly in the context of telling the time).
How does a fraction represent a proportion of a unit?
Proportion - A comparative part of a quantity or set. A proportion (such as 4 out of 10) can be expressed as a fraction (2/5), as a percentage (40%) or as a decimal (0.4).
This terminology can be used in two different ways but here we are using it to refer to a share or a part of something.
3.g. 3/8
Introduce fraction notation as meaning a number of equal parts of a unit, making particular use of pizzas (circles) and chocolate bars (rectangles) in the explanation. In this interpretation, the fraction p/q means ‘divide the unit into q equal parts and take p of these parts’.
When explaining fractions, be careful about using the word ‘whole’ as a noun: try to use it only as an adjective, for example ‘three eighths of a whole pizza’.
How does a fraction represent a point on a line?
In Figure 15.2, the section of the number line between 0 and 1, which is 1 unit in length, has been divided up into eight equal sections. Each of these sections is one-eighth of a unit. So, the points from 0 to 1 can be labelled as 0, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 and 1. Notice also that each step marked along this section of the number line can be thought of as an eighth: so 3/8 would also be represented by the step from 0 to the point 3/8; or, indeed, by the step from 2/8 to 5/8, and so on. This image of a step along a number line is helpful when making sense of the addition and subtraction of fractions.
How does a fraction represent a proportion of a set?
The idea of the fraction 3/8 as meaning 3 parts selected from 8 parts of a unit can then be extended to a proportion of a set. This is the way it is used in situations where a set of items is subdivided into eight equal subsets and three of these subsets are selected. For example, the set of 40 dots in Figure 15.3(a) has been subdivided into eight equal subsets (of 5 dots each) in Figure 15.3(b). The 15 dots selected in Figure 15.3(c) can therefore be described as three-eighths of the set of 40. So, the diagram shows that one-eighth of 40 is 5 and three-eighths of 40 is 15.
How does a fraction represent a division?
The fraction 3/8 can also be used to represent the division of 3 by 8, thinking of division as ‘equal sharing between’
what we see here is, first, that the symbols 3/8 can mean ‘divide 3 units by 8’ and, second, that the result of doing this division is ‘three-eighths of a unit’. Hence, the symbols 3/8 represent both an instruction to perform an operation and the result of performing it! We often need the idea that the fraction p/q means ‘p divided by q’ in order to handle fractions on a calculator. Simply by entering p ÷ q we can express the fraction as a decimal. This also allows us to use fraction notation as an alternative to the division sign (÷). You will find, therefore, that the division sign itself is used less and less beyond primary school mathematics, so that, for example, ‘450 divided by 25’ will often be written as 450/25. This is certainly the case in algebra, where division (x ÷ y) is almost always indicated by fraction notation (x/y).
Introduce older children in primary school to the use of fractions to compare one quantity with another (that is, finding the ratio), especially in the context of prices. For example, we can compare two prices of £9 and £12 by stating that one is three-quarters of the other.
How does a fraction represent a ratio?
because the symbols 3/8 can mean ‘three divided by eight’, we can extend the meanings of the symbols to include ‘the ratio of three to eight’. This is sometimes written as 3:8. For example, in Figure 15.5(a), when comparing the set of circles with the set of squares, we could say that ‘the ratio of circles to squares is three to eight’. This means that for every three circles there are eight squares. Arranging the squares and circles, as shown in Figure 15.5(b), shows this to be the case. The reason why we also use the fraction notation (3/8) to represent the ratio (3:8) is simply that another way of expressing the comparison between the two sets is to say that the number of circles is three-eighths of the number of squares. Rational numbers are given that name because they can be expressed as the ratio of two integers. So, the principle that any fraction can be understood as a ratio is a really fundamental idea – indeed, mathematically, this is probably the most important meaning of a fraction.
What about numerators, denominators, vulgar fractions, proper and improper fractions, mixed numbers, and so on?
Numerator - The top number in a fraction.
Denominator - The bottom number in a fraction.
The numerator and the denominator are simply the top number and the bottom number in the fraction notation. So, for example, in the fraction 3/8 the numerator is 3 and the denominator is 8.
The fraction notation for parts of a unit can also be used in a situation where there is more than one whole unit to be represented. Altogether here, we have eleven-eighths of a pizza, written 11/8. Since eight of these make a whole pizza, this quantity can be written as 1 + 3/8, which is normally abbreviated to 13/8. This is called a mixed number.
Mixed number - A way of writing a fraction greater than 1 as a whole number plus a proper fraction. For example, 18/5 as a mixed number is 33/5 (three and three-fifths).
Proper fraction - A fraction in which the top number is smaller than the bottom number; a fraction less than 1.
Improper fraction - A fraction in which the top number is greater than the bottom number; a fraction greater than 1; informally, a top-heavy fraction.
Proper fractions are therefore those that are less than 1, with improper fractions being those greater than 1. We could refer to improper fractions more informally as ‘top-heavy fractions’.
A prerequisite for being able to change an improper fraction into a mixed number (or vice versa) is to understand that, for example, 8/8 is equal to 1, 16/8 is equal to 2, 24/8 is equal to 3, and so on. This is easy to explain using chocolate bars or pizzas, but grasping the principle here should be a specific focus for teaching about fractions.
What are equivalent fractions?
The concept of equivalence – which we saw in Chapter 3 to be one of the fundamental processes for understanding mathematics – is one of the key ideas for children to grasp when working with fractions. Using the first idea of a fraction above, that it represents a part of a unit, it is immediately apparent from Figure 15.8, for example, that three-quarters, six-eighths and nine-twelfths all represent the same amount of chocolate bar. This kind of ‘fraction chart’ is an important teaching aid for explaining the idea of equivalence.
Equivalent fractions - Two or more fractions that represent the same part of a unit or the same ratio. For example, 2/3, 4/6, 6/9, 8/12 are all equivalent fractions.
Sequences of equivalent fractions follow a very straightforward pattern. For example, all these fractions are equivalent: 3/5, 6/10, 9/15, 12/20, 15/25, 18/30, 21/35, 24/40, and so on.
The numbers on the top and bottom are simply the 3-times and 5-times tables, respectively. This means that, given a particular fraction, you can always generate an equivalent fraction by multiplying the top and the bottom by the same number; or, vice versa, by dividing by the same number. So, for example:
4/7 is equivalent to 36/63 (multiplying top and bottom by 9).
40/70 is equivalent to 4/7 (dividing top and bottom by 10).
Equivalence of fractions is one of the most important ideas to get across to children in primary school. Get them to make a variety of fraction charts (like the one in Figure 15.8) and then to find various examples of equivalent fractions.
How do you simplify fractions?
Simplifying fractions: by dividing the top and bottom numbers by any common factors, we can reduce the fraction to its simplest form. This process is often called ‘cancelling’.
Cancelling - The process of dividing the top number and the bottom number in a fraction by a common factor to produce a simpler equivalent fraction.
For example, 6/8 can be simplified to the equivalent fraction 3/4 by dividing top and bottom numbers by their highest common factor, 2 (cancelling 2). Similarly, 12/18 can be simplified to the equivalent fraction 2/3 by cancelling 6, which is the highest common factor
How does this work with ratios?
The principle used for simplifying fractions applies to ratios, of course, because fractions can be interpreted as ratios. If you multiply or divide two numbers by the same thing, the ratio stays the same.
e.g. the ratio 28:32 can be simplified to the equivalent ratio of 7:8 (dividing both numbers by 4). This means that one price is 7/8 (seven-eighths) of the other.
Equivalent ratios - Different ways of expressing the same ratio; for example, the ratio 30:50 can be written as the equivalent ratio 3:5.
How do you compare one fraction with another?
The first point to notice here is that when you increase the bottom number of a fraction you actually make the fraction smaller, and vice versa. Consider, for example, what are called unit fractions. These are fractions with numerator ‘1’: a half (1/2), a third (1/3), a quarter (1/4), a fifth (1/5), a sixth (1/6), and so on. Important in developing mastery in fractions is to understand that 1/2 is greater than 1/3, which is greater than 1/4, which is greater than 1/5, and so on. This is very obvious if the symbols are interpreted in concrete terms, as bits of pizza or a chocolate bar, for example. Interpreting these unit fractions as points on a number line, as shown in Figure 15.9, also makes it clear that they get smaller as the bottom number gets larger, because the points representing these unit fractions are getting closer to zero. It is very easy for a child to get this wrong, of course, if they simply look at the numbers involved in the fraction notation without thinking about what they mean.
Then, second, there is no difficulty in comparing two fractions with the same bottom number. Clearly, five-eighths of a pizza (5/8) is more than three-eighths (3/8), for example.
Generally, to compare two fractions with different bottom numbers we may need to convert them to equivalent fractions with the same bottom number. This will have to be a common multiple of the two numbers. It might be (but does not have to be) the lowest common multiple. For example, which is greater, seven-tenths (7/10) of a chocolate bar or five-eighths (5/8)? The lowest common multiple of 10 and 8 is 40, so convert both fractions to fortieths:
7/10 is equivalent to 28/40 (multiplying top and bottom by 4); and
5/8 is equivalent to 25/40 (multiplying top and bottom by 5).
How is a remainder in a division calculation interpreted as a fraction?
Take an example: 30 ÷ 7 = 4 remainder 2. Depending on the context in which this division calculation arose, it may be possible to deal with the remainder here by dividing that by 7 as well. Using the idea that a fraction can represent a division, we know that 2 ÷ 7 is equal to 2/7. So we might give the result of the division as a mixed number: 42/7. This would be a possible answer if the original (rather artificial) problem had been to find out how much chocolate each person gets if 30 bars are shared equally between 7 people: answer, 42/7 bars each! It would not be an appropriate answer, however, if the question had been, ‘how many vans do you need to transport 30 children if each van holds 7 children?’, because you cannot have 2/7 of a van.
Show older children in primary school how the remainder in a division can also be divided by the divisor. For example: 51 ÷ 4 = 12 remainder 3. If the remainder is then divided by 4 (giving 3 ÷ 4 = 3/4), the result is 123/4. Discuss a range of real-life contexts in which this might be an appropriate solution and when it would not.
How do you add and subtract fractions?
First, to add two fractions with the same bottom number (denominator) is very simple. Just visualize the fractions as parts of a whole unit. So, for example, if you have one-eighth (1/8) of a chocolate bar and you add it to three-eighths (3/8) of a chocolate bar, you have altogether four-eighths (4/8) of a chocolate bar. So, clearly, 1/8 + 3/8 = 4/8. This answer can then be simplified to 1/2 by cancelling 4.
Subtraction is equally straightforward when the two fractions have the same denominator. For example, if you have seven-eighths of a pizza and eat five-eighths then you are left with two-eighths. Recording this in fraction notation, 7/8 – 5/8 = 2/8. This result could, of course, be simplified to 1/4 by cancelling 2.
Sometimes, when adding two or more proper fractions, the result may be an improper fraction. For example, 3/8 + 5/8 + 7/8 = 15/8. This result could then be expressed as a mixed number (17/8).
To add or subtract two fractions with different denominators is a bit trickier. Before attempting to combine the fractions, you have to change one or both of them to equivalent fractions so that they finish up with the same bottom number – it’s best to use the lowest common multiple for this.
So, for example, to add 1/6 and 1/2, we would spot that the 1/2 is equivalent to 3/6, so both fractions can be expressed as sixths. We go for sixths because 6 is the lowest number that is a multiple of both 2 and 6. In this context, the lowest common multiple of the two denominators is often called the ‘lowest common denominator’. The calculation then looks like this: 1/6 + 1/2 = 1/6 + 3/6 = 4/6 (= 2/3).
Here is an example with subtraction: how much more is 2/3 of a litre than 1/4 of a litre? This requires the calculation 2/3 − 1/4. To do this, we change both fractions to twelfths, because 12 is the lowest common multiple of 3 and 4. The 2/3 of a litre is equivalent to 8/12 of a litre; and the 1/4 of a litre is equivalent to 3/12 of a litre. The difference between 8/12 of a litre and 3/12 of a litre is clearly 5/12 of a litre. Written down, the calculation looks like this: 2/3 − 1/4 = 8/12 − 3/12 = 5/12.
A common error in adding fractions is to add the top numbers and add the bottom numbers; for example: 1/5 + 3/5 = 4/10. This error only occurs when the learner just responds to the symbols mindlessly without any attempt to connect them to a visual image that makes sense of the fractions. In this case, the correct addition is: 1/5 + 3/5 = 4/5 (one-fifth of a pizza plus three-fifths of a pizza is equal to four-fifths of a pizza).
A prerequisite for being able to add or subtract fractions with different denominators is the ability to identify the lowest common multiple of two (or more) numbers. Aim to develop mastery of this skill before children move on to identifying the lowest common denominators in the process of the addition and subtraction of fractions.
How do you multiply two simple fractions?
The process for multiplying two fractions can be understood in visual terms by applying the fractions to the area of a square, as shown in Figure 15.10(a). The square has been divided into thirds by the horizontal lines in Figure 15.10(b) and then divided into quarters by the vertical lines drawn in Figure 15.10(c). The square has now been divided into twelfths. Using the idea that the area of a rectangle is given by the product of the two sides, it is now clear that the area of the shaded rectangle in Figure 15.10(d) is equal to 2/3 multiplied by 3/4. Since this area is six twelfths, we have shown that 2/3 × 3/4 = 6/12. (This can then be cancelled down to 1/2.)
Note that we get twelfths in Figure 15.10(c) because we have 3 sections horizontally and 4 sections vertically. This is effectively multiplying together the denominators of the 2/3 and 3/4. And we get 6 of these twelfths shaded in Figure 15.10(d) because the shaded rectangle arises from 2 of the horizontal sections and 3 of the vertical sections. This is effectively multiplying together the numerators of the 2/3 and 3/4. So, there is a very simple rule for multiplying two fractions: multiply the two denominators and multiply the two numerators! Then give the answer in the simplest form, by cancelling.
Finally, in this example, notice that the shaded rectangle in Figure 15.10(d) can be thought of as two-thirds of three-quarters of the square; or as three-quarters of two-thirds of the square. The word of in the language pattern ‘a fraction of something’ is helpfully connected with the symbol of multiplication. So, for example, the fact that 2/3 of 60 is 40 can also be expressed as 2/3 × 60 = 40. Similarly, 1/2 × 1/4 can be understood as: what is a half of a quarter?
A key principle in teaching for mastery of fractions: make explicit and help children to understand the equivalence of, for example, these three statements:
1/5 × 30 = 6
1/5 of 30 = 6
30 ÷ 5 = 6
What other calculations with fractions should I be able to do?
Addition with mixed numbers
(a) 31/5 + 23/5
= 3 + 1/5 + 2 + 3/5 (separating the whole number parts and fractional parts)
= 5 + 4/5 (adding the whole numbers and the fractions separately)
= 54/5 (writing this as a mixed number)
(b) 34/5 + 23/5
= 3 + 4/5 + 2 + 3/5 (separating the whole number parts and fractional parts)
= 5 + 7/5 (adding the whole numbers and the fractions separately)
= 5 + 1 + 2/5 (changing the improper fraction to a whole number and a fraction)
= 6 + 2/5 (adding the 1 to the 5)
= 62/5 (writing this as a mixed number)
Subtraction with mixed numbers
(a) 54/5 − 33/5
Think of this as (5 + 4/5) − (3 +3/5)
First deal with the fractional parts: 4/5 − 3/5 = 1/5
Then deal with the whole number parts: 5 − 3 = 2
Combining these as a mixed number, we get 54/5 − 33/5 = 21/5
(b) 52/5 − 33/5
Think of this as (5 + 2/5) − (3 + 3/5)
This will require the use of a form of decomposition (see subtraction methods in Chapter 9).
First look at the subtraction with the fractional parts: 2/5 − 3/5; this would give a negative result.
So, exchange 1 from the 5 for five-fifths: 5 + 2/5 = 4 + 1 + 2/5 = 4 + 5/5 + 2/5 = 4 + 7/5
We can now complete the subtraction, using the method in (a):
(4 + 7/5) − (3 + 3/5) = 14/5
Divisions with fractions
(a) Calculate 4/5 ÷ 3
Remember that dividing by 3 is the same thing as finding a third of something, which is the same as multiplying by 1/3.
So, 4/5 ÷ 3 = 1/3 × 4/5
= 4/15 (using the method for multiplying fractions explained earlier in the chapter).
p.240
(b) Calculate 20 ÷ 1/4
Remember that the result of a division is unchanged if both numbers are multiplied by the same thing (see mental and informal strategies for division in Chapter 11).
So, multiply both numbers in 20 ÷ 1/4 by 4. (Remember that 4 quarters = 1.)
Then we get 20 ÷ 1/4 = 80 ÷ 1, which is just 80.
The result in (b) makes a lot of sense if you think of the division as the inverse of multiplication. For example, how many quarters of a pizza can you get from 20 pizzas? You can now ask your friends what is twenty divided by a quarter and then enjoy explaining to those who give the answer 5 why the answer is 80!
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Catholic Publishing: A Game for Suckers
It’s a typical morning at Sophia Institute Press headquarters. Panting from my daily hike up the six flights of worn and uneven stairs that lead to our warehouse and office space—the penthouse suite of a semi-renovated nineteenth-century mill—I reach my desk and turn on the computer. Five new intra-office e-mails greet me, which can mean only one thing: publisher, marketing, and editorial (me) are still fighting over a book title.
Past title wars are the stuff of legend around here, and this one has all the earmarks of becoming one for the annals. The author of this particular book, about Catholic family life, supplied his own title, but it never won any backers on our end. Now the manuscript is almost ready to go, but the lack of a title is holding up the works: copyright paperwork, cover art, prepublication promotion, all dependent on the final title. We thought we’d hit on a good one a few weeks ago, but it didn’t stick. After that we’d brainstorm sporadically—in impromptu meetings, via e-mail, over the water cooler. But we got no closer, and the latest messages on my computer don’t contain any breakthroughs. So this morning we gather in one room, close the door, and instruct warehouse staff not to let us out until we’ve picked a title or died trying.
Publisher suggests a title that plays on the name of a fifties Beat Generation poem. "Wrong audience," replies marketing. "This book is written specifically for people who’ve never heard of Kerouac." He counters with a punchy two-worder taken from a theme in the book’s introduction.
Now it’s publisher’s turn to object. "A short title would allow you to have nice big letters on the spine," he concedes, "but this one doesn’t really tell you what the book is about. It could be Catholic family life, or it could be Oprah’s latest diet book."
I step into the breach with a particularly snappy title that came to me that morning as I was brushing my teeth. There’s a pause."That’s just stupid," publisher and marketing say together.
And so it goes.
Eventually we do break for lunch and attend to other matters. I wrestle with some editing for an hour. I send off another futile e-mail to a writer who took an advance from us then went incommunicado. I peck away at the mountain of proposals and unsolicited manuscripts on the desk behind me. The day is slipping away, and we still have this poor little book without a name.
Then, later that afternoon, I wander past publisher’s desk. Why, I ask, couldn’t we pull a key adjective out of a subtitle that he’d tried unsuccessfully to mate with an early main-title prototype and add it to marketing’s short, punchy suggestion? That would sufficiently identify it for our readers, and the rest of the subtitle would slide in quite neatly—even euphoniously—behind it.
He types it on the screen, and we both stare as if in a trance. The tumblers in our brains begin to click in unison.
"I like it if you like it," publisher says finally. "Seriously, do you like it?" I say I do. We buzz over to marketing. He likes it if we like it.
We have a title. Send up the white smoke. I get home that evening, and my wife asks me how I can look so ragged and beaten when all I do is read books all day.
* * *
The fact is that such contests of intellect and will aren’t the only.aspects of this business that gray the hairs and angry up the blood. Catholic publishing is a game for suckers. There’s no glamour in it. No wining and dining of authors, no junkets to exotic locales to scout new writing talent. My business card is not a ticket to free upgrades and courtside seats.
Our sales goals are modest. Catholics do not read religious books in significant numbers anymore—excepting turgid novels about Vatican conspiracies or the end times. Five thousand copies of a title sold in a year is a successful run for us; this past summer The Da Vinci Code routinely would triple that number on a bad day.
And yet, we wouldn’t publish the next Da Vinci even if it fell in our laps. Like many other Catholic publishers, we are a hybrid of business and apostolate, constantly striving to balance the twin goals of building up the kingdom of God and making enough money to pay the printers, the electric company, and the staff. Another Da Vinci might make us rich beyond dreams of avarice but at the cost of betraying the apostolate and its aims. But trying to sell large numbers of sound, orthodox Catholic books today is at best a dubious business proposition. We’re offering a product that few people want and most don’t realize they need.
Not long ago, I helped man a table full of our best-selling books at a fundraising fair for my fairly active, solid, middle-class parish. We had a prominent location in "Ministry Alley" and a large sign announcing that 100 percent of the profits would go to the parish’s Respect Life group. After two days, thousands of passers-by, and hours of shameless hawking, we sold a grand total of two books.
If this episode is by itself not proof of much, it is at least suitably iconic. Our market is a niche, and that niche comprises only a sliver of the millions of Catholics sitting in the pews—or for that matter, teaching CCD, attending Bible study, and baking muffins for the women’s sodality. Blame the many distractions of the modern media if you want, blame the catechetical vacuum of the last forty years, blame the Freemasons: Catholics aren’t reading. The market for good Catholic books of spirituality, apologetics, and popular theology—again, we’re not talking Andrew Greeley or The Prayer of Jabezhere—is by all comparisons tiny. (For the next fundraiser, the Respect Life group offered boxes of Krispy Kreme donuts as the Boy Scouts did. They sold out in two hours.)
* * *
Of course, a generation or three ago, when the Church in America had really come into its own, the English-speaking world enjoyed an unprecedented richness of Catholic books. It was love for those fine old books and a desire to re-introduce them to a modern audience that would lead former philosophy professor John Barger, in 1983, to set up Sophia Institute Press in his basement in Manchester, New Hampshire. Beginning with Dietrich von Hildebrand’s Marriage: The Mystery of Faithful Love, Barger and Sophia would go on to develop a reputation for resurrecting forgotten Catholic classics: hunting down forgotten works of theology, philosophy, and spirituality, and then, most importantly, editing them to modern standards of readability. New titles, contemporary fonts and layout design, and attractive covers typically complete the resurrection.
In recent years, Sophia began adding to its catalogue new books by living authors, and today roughly a third of the twenty-four-some books we publish each year are new titles by current authors. In 1993, the company moved from the publisher’s basement to its current riverside offices in one of Manchester’s many converted textile mills. No longer a one-man operation, today we’d be considered a small-midsize publishing house, subsisting on just over $1 million in sales and another $150,000 in benefactor donations each year.
As editor, I am primarily responsible for acquisitions and editing tasks: from evaluating proposals and manuscripts (and writing polite rejections to well-meaning folks who send us stuff like Thoughts and Meditations on God, Volume One) to working with authors to fine-tune their concepts and prettify their prose. During every stage of developing a manuscript for publication, I try to keep one question before me at all times: What about this book would compel someone to pick it up? In many ways, the evolution of a book works backwards: from the sale to marketing efforts to at least an initial vision of the cover and title and then finally to the concept and the text. Beginning with the end in mind keeps us ever-conscious of the needs and wishes of the members of our niche market.
Staying true to our dual identity as business and apostolate—striving to give our audience what they want as consumers yet what they need as Catholics—sometimes calls for tricky balancing acts and strategic compromises. Although most members of our orthodox and socially conservative Catholic readership probably wouldn’t be too tempted by Greeley-style schlock or another Left Behind clone, in our market there are other types of books that might sell but nonetheless would be illicit for us to publish. We might be able, for instance, to sell large numbers of books harshly and uncharitably indicting certain bishops—say, the liberals or the homosexual/pedophile coddlers. With other readers we might have great success peddling sensationalistic accounts of the latest reported private revelations.
But we couldn’t do these things while remaining faithful to our mission and principles. So when considering manuscripts our calculation doesn’t end (as it would for a strictly business publisher) with what the audience wants—that is, what would sell. We have to ask ourselves: What good will this do the Church?
On the other hand, neither can the question of our readers’ spiritual needs be the sole criterion. Many an unsolicited manuscript has landed on my desk topped with a cover letter announcing that every Catholic in America needs to read this book! Embedded in each is some message guaranteed to make the reader happier, holier, and closer to God. They can be rich in Scripture, steeped in the wisdom of the early Church Fathers, and suffused with the piety and sincerity of the author.
And we’d be lucky, in a year, to sell enough to pay the initial printing costs. If most people had the intellectual clarity to know just what they needed and then the supernatural integrity to want it, we wouldn’t have an out-of-print list filled with so many wise, edifying, and unsalable books. As it is, our business, like all others, is subject to the ravages of original sin. And so our challenge is to fulfill the mission of our apostolate by publishing books that Catholics need to read—books that will help them better to know, love, and serve God—packaged and presented in way that will make Catholics want to read them. This helps us sell enough books to support the business, and it also further serves the goals of the apostolate: If we publish good Catholic books that almost no one will buy and read, we’re just hiding our light under a bushel.
But "spiritually beneficial" and "compelling to the buyer" still aren’t enough. In addition to these qualities, we look for manuscripts that are unique in some way. Until some enterprising author discovers a fourth person of the Trinity, there will be precious little new under the sun in Catholic publishing. Why should a Catholic bookstore browser buy this book on the rosary and not one of the hundred others that have come before it? How is this Defense of the Catholic Faith or that Learn How to Pray Better going to stand out on shelves and in catalogues stuffed with dozens of similar titles? Show an editor something really and truly different, and you will have caught his attention. (Although, sometimes we get proposals for books so different they border on—or cross over to—the downright bizarre.)
Sophia founder and publisher John Barger is fond of reminding us that a new book is published every three minutes, around the clock. If our books can’t distinguish themselves in the overcrowded marketplace, if they can’t offer readers unique and compelling benefits, then both the business and the apostolate are likely to fail.
* * *
Of course, as editor you can pore over a manuscript and subject it to every test. You can deem it unique, compelling, and beneficial beyond question. You can read the market perfectly. You can slap on an inspired title and an arresting cover. You can publish it with fanfare—only to watch it flop spectacularly. In a couple of years, all those leftover copies of the book you thought would change the world will be turned into fireplace starter logs and blown insulation.
In fact, some of our most notable failures have been books we were high on at printing time, books that I still consider among the best I’ve edited. A year and a half ago, for example, we published Adventures in Orthodoxy, a delightful Chestertonian waltz through the articles of the Creed, written by popular convert-apologist (and This Rock contributor) Dwight Longenecker. Never dull and at times brilliant, it was written with more stylistic flair than any manuscript that’s ever made its way out of my office. Beneficial spiritual insights galore. Unique? Show me another book like it. We gave it what we thought was a provocative cover—featuring an Indiana Jones-like explorer reaching to open the door of a church—and turned it loose on the masses.
The masses shrugged.
Why? Did we misjudge our modern Catholic audience’s appetite for the whimsical religious essays of a Chesterton-lite? Did we fail to promote it adequately? Or could it have been the title or the cover? In the past we’ve been able to turn some flops (or at least sleepy sellers) into hits by reprinting them with new looks and names. Perhaps a similar treatment someday will give Longenecker’s book the success it deserves.
Conversely (and happily), sometimes the hundred-to-one shot gallops home; the stone that the builders rejected, as P. G. Wodehouse put it, becomes the main thing. That is, a book for which we had only modest hopes turns into a bona fide hit. Such has been the case just recently with A Mother’s Rule of Life by Holly Pierlot. We saw in it a fine little book that borrows from the wisdom of religious life to help Catholic moms organize their households and fulfill their vocations as wives and mothers. But we never reckoned on the rave responses it would receive from readers and the extensive word-of-mouth promotion among Catholic mothers’ groups and homeschoolers that would drive it to the top of our bestseller lists. It has opened our eyes to one of the hottest genres in our niche market: what one observer has dubbed "mom lit." Currently we are striking out for the first time in the direction of original children’s fiction. Children’s books are reliable sellers, and the word from bookstores is that Catholic parents continue to ask for kids’ books that are unambiguously Catholic and catechetical yet entertaining. We’ll take our first few tentative steps into this market later this year and next, and their success or failure will help guide future decisions. I for one am guardedly hopeful, if only because it would make my job easier. Half, if not more, of the proposals and manuscripts I receive are for children’s books!
* * *
Through all the unexpected hits and misses, notwithstanding every failure of our best-laid plans, we try to stay positive. Catholic publishing is a game for suckers, and that’s a relief—it means that our bottom line isn’t to be found on the sales sheet. It means we can hope for incalculable profits.
We do work hard to focus our resources, talents, and experiences shrewdly and wisely; we do try all we can to jigger the game in a way that we believe will increase our odds for success. But in the end, it’s God’s work, and doing God’s work means recalibrating your measure of success. What began as one man’s labor of love has become an entire company’s daily act of faith.
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