Arithmetic - GED Math

1. What is $-4.5 + 7.25$?

   2.75. The signs differ, so subtract the absolute values (7.25 minus 4.5) and keep the sign of the number with the larger absolute value.

2. What must two fractions have before you can add or subtract them?

   A common denominator. Then add or subtract the numerators and keep the denominator.

3. What is $\frac{3}{4} - \frac{1}{6}$?

   $\frac{7}{12}$. With denominator $12$: $\frac{9}{12} - \frac{2}{12} = \frac{7}{12}$.

4. What is $\frac{2}{3} \div \frac{4}{9}$?

   $\frac{3}{2}$. Multiply by the reciprocal: $\frac{2}{3} \times \frac{9}{4} = \frac{18}{12} = \frac{3}{2}$.

5. What is the order of operations?

   Parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right).

6. Evaluate $12 - 8 \div 4 \times 2$.

   $8$. Work division and multiplication left to right: $8 \div 4 = 2$, $2 \times 2 = 4$, then $12 - 4 = 8$.

7. What is $-\frac{3}{4} \times \frac{8}{9}$?

   $-\frac{2}{3}$. Multiply across: $-\frac{24}{36} = -\frac{2}{3}$. One negative factor makes the product negative.

8. What is $0.6 \times 0.05$?

   0.03. Multiply $6 \times 5 = 30$, then place three decimal places in all: 0.030, which is 0.03.

9. How do you divide by a fraction?

   Multiply by its reciprocal. For example, $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.

10. What is $-8 - (-5)$?

    $-3$. Subtracting a negative is the same as adding: $-8 + 5 = -3$.

11. What is the sign of the product of two negative numbers?

    Positive. Two negatives multiplied or divided give a positive; one negative gives a negative.

12. Write $2\frac{3}{5}$ as an improper fraction.

    $\frac{13}{5}$. Multiply the whole number by the denominator and add the numerator: $2 \times 5 + 3 = 13$.

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