Multiplying and Dividing Rational Numbers

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Front

How do you multiply two fractions?

Back

To multiply two fractions, multiply the numerators together and the denominators together. For example, (a/b) * (c/d) = (a*c)/(b*d).

Front

What is the result of multiplying a fraction by a whole number?

Back

To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number and keep the denominator the same. For example, 3 * (2/5) = (3*2)/5 = 6/5.

Front

How do you divide a fraction by a whole number?

Back

To divide a fraction by a whole number, multiply the denominator of the fraction by the whole number. For example, (2/3) ÷ 4 = 2/(3*4) = 2/12 = 1/6.

Front

What is the reciprocal of a fraction?

Back

The reciprocal of a fraction is obtained by flipping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3.

Front

How do you divide by a fraction?

Back

To divide by a fraction, multiply by its reciprocal. For example, 5 ÷ (1/2) = 5 * (2/1) = 10.

Front

What is the relationship between multiplication and division of rational numbers?

Back

Multiplication and division are inverse operations. Dividing by a number is the same as multiplying by its reciprocal.

Front

If you have 1/4 mile and each runner runs 1/16 mile, how many runners are needed?

Back

4 runners are needed because 1/4 ÷ 1/16 = 1/4 * 16/1 = 4.

Front

How do you find the cost of multiple items at a unit price?

Back

Multiply the unit price by the number of items. For example, if peaches cost $2.50 per pound and you buy 3 pounds, the total cost is $2.50 * 3 = $7.50.

Front

What is the formula to find the number of pieces you can cut from a length?

Back

To find the number of pieces, divide the total length by the length of each piece. For example, 9 ft ÷ (2/3) ft = 9 * (3/2) = 13 pieces.