Question

In Exercises 103–110, insert either , or = in the shaded area to make a true statement. 8/13÷8/13 □ |−1|

Accepted Answer

Step 1: Simplify the left-hand side of the inequality. The expression is $$ \frac{8}{13} \div \frac{8}{13} . $$Recall that dividing fractions involves multiplying by the reciprocal of the second fraction. This means $$ \frac{8}{13} \div \frac{8}{13} = \frac{8}{13} 	imes \frac{13}{8} . $$Step 2: Multiply the numerators and denominators of the fractions. $$ \frac{8}{13} 	imes \frac{13}{8} = \frac{8 \cdot 13}{13 \cdot 8} . $$Simplify the fraction by canceling out the common terms in the numerator and denominator, which results in $$ 1 . $$Step 3: Simplify the right-hand side of the inequality. The expression is $$ | -1 | $$, which represents the absolute value of $$ -1 . $$Recall that the absolute value of a number is its distance from zero on the number line, so $$ | -1 | = 1 . $$Step 4: Compare the simplified left-hand side and right-hand side. The left-hand side is $$ 1 $$, and the right-hand side is also $$ 1 . $$Step 5: Insert the appropriate symbol ($$ = ) in $$the shaded area to make the statement true. The final inequality is $$ \frac{8}{13} \div \frac{8}{13} = | -1 | .$$

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 8/13÷8/13 □ |−1|

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Key Concepts

Division of Fractions

Absolute Value

Inequality Symbols