To reduce two or more fractions whose denominators are unlike to equivalent fractions having their least common denominator:

9

1. Reduce, %, and 7 to equivalent fractions having their least common denominator.

OPERATION

The 1. c. m. of 30, 40, and 60 is 120

RULE.

Find the 1. c. m. of the denominators; then change each fraction to an equivalent fraction having the 1. c. m. for its denominator.

Reduce each of the following groups to equivalent fractions having their least common denominator:

Remembering that the g. c. d. of two numbers is never greater than their difference, reduce the following to their lowest terms:

k. Without dividing, tell how many times 25 is contained in 4275.

371

7. Reduce

to its simplest form.*

621

* Divide the numerator and the denominator by 1, and reduce the fraction thus obtained to its lowest terms. Or, divide the numerator and the denominator by 121.

To find the sum of two or more fractions:

1. Add 1, 3, and 58.

OPERATION

(1) The 1. c. m. of 45, 30, and 60 is 180.

NOTE. If the work that precedes this article has been well done, no explanation of the foregoing will be necessary. Pupils have already learned (presumably before using this book) (1) that fractions may be reduced to higher terms, (2) that two or more fractions whose denominators are not alike may be reduced to higher terms with like denominators, (3) that a common denominator of two or more fractions with unlike denominators is a common multiple of the given denominators, and (4) that in reducing a fraction to higher terms the numerator and denominator must be multiplied by the same number. The simple problem of adding 44 180ths, 102 180ths, and 159 180ths is not unlike the problem of adding 44 apples, 102 apples, and 159 apples.

RULE. Reduce the fractions, if necessary, to equivalent fractions having a common denominator, add their numerators, and write their sum over the common denominator.

k. Find the sum of the ten sums, a to j.

RULE.

Reduce the fractions, if necessary, to equivalent fractions having a common denominator, find the difference of their numerators, and write it over the common denominator.

g. Find the sum of the six differences, a to f.

h. From 385 subtract 141.

j. From 46 subtract 251.

i. 548-122%

k. 323-261

How

7. From a piece of land containing 363 acres there were sold two lots, each containing 36 acres. many acres remained unsold?

m. Mr. Jones owned 47 acres of land. He sold 153 acres. How many acres did he then have?

n. Mr. George owns 95 acres. Mr. Henry owns 482 acres. Mr. George owns how many acres more than Mr. Henry?

To subtract one mixed number from another when the fraction in the subtrahend is greater than the fraction in the minuend:

k. Find the sum of the ten differences, a to j.

y. Find the sum of the thirteen results, 7 to x.

are 6 times as many parts as there are in, and that the parts are of the same size as those in

7

Observe that by the second operation we obtain ; that in there are the same number of parts as there are in, and that the parts are 6 times as great as those in 4.

RULE. Multiply the numerator or divide the denomi nator by the integer.

m. Find the sum of the twelve products, a to l.

z. Find the sum of the twelve products, n to y.

Find the cost of:

aa. 240 eggs at of a cent each. bb. 144 pens at § of a cent each.

cc. 175 apples at of a cent each.