Math Word Problems for CBEST Exam Study Guide
The directions for the word problem game are simple: While carefully observing a word problem, find all the math words and numbers in the problem. Eliminate the nonessential words and facts in order to find your answer.
Operations in Word Problems
To prepare for the game, make five columns on a sheet of paper. Write one of these words on the top of each column: Add, Subtract, Multiply, Divide, Equals. Now try to think of five words that tell you to add, five that tell you to subtract, and so on. If you can think of five for each column, you win the first round. If you can't think of five, you can cheat by looking at the following list.
- How did you do?
- 0 = keep studying
- 1–3 for each = good
- 4–6 for each = great
- 7+ for each = excellent
- Add: sum, plus, more than, larger than, greater than, and, increased by, added to, in all, altogether, total, combined with, together, lengthened by
- Subtract: difference, minus, decreased by, reduced by, diminished by, less, take away, subtract, lowered by, dropped by, shortened by, lightened by, less, less than, subtracted from, take from, deducted from. Note: The words in bold are backwardswords. (See the next section.)
- Multiply: product, times, of, multiplied by, twice, thrice, squared, cubed, doubled, tripled, rows of, columns of
- Divide: quotient of, ratio of, halved, per, split, equal parts of, divided by, divided into, reciprocal Note: The words in bold are backwardswords. (See the following section.)
- Equals: is, equal to, the same as, amounts to, equivalent to, gives us, represents
Backwardswords are words in a word problem that tend to throw off test takers; they indicate the opposite of the order in which the numbers appear in the problem. Only subtraction and division have backwardswords. Addition and multiplication come out the same no matter which number is written first: 2 + 6 is the same as 6 + 2, but 2 – 6 is not the same as 6 – 2. Using the numbers 10 and 7, notice the following translations:
- 10 minus 7 is the same as 10 – 7
- 10 take away 7 is 10 – 7
- 10 less 7 is the same as 10 – 7
- But 10 less than 7 is the opposite, 7 – 10
- 10 subtracted from 7 is also 7 – 10
Four Success Steps for Converting Words to Algebra
In order to make an equation out of words, use these steps:
- Find the verb. The verb is always the = sign.
- Write in the numbers.
- Write in the symbols for the other code words. Be careful of backwardswords.
- If necessary, add parentheses.
- 10 over 7 is written
- The quotient of 10 and 7 is
- But 10 divided into 7 is written
- And the reciprocal of is
When setting up division problems in algebra, avoid using the division sign: ÷. Instead, use the division line: .
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