Question

Write a sum, difference, product, and quotient whose answers could all have an estimate of about 6. One expression should include only mixed numbers, one expression should include only decimals, one expression should include only negative rational numbers, and one expression should include only positive rational numbers. When do you round up a rational number? When do you round down?

A. Sum: 3.5 - 0.5 Difference: 5.5 - 0.5 Product: -2.5 * -2 Quotient: 3 / 0.5
B. Sum: 6.2 + 0.8 Difference: 7 - 1 Product: -1.5 * -4 Quotient: 9 / 1.5
C. Sum: -2 + 8 Difference: -3 - 3 Product: -0.5 * -12 Quotient: -6 / 1
D. Sum: 2/3 + 4/3 Difference: 1.1 - 0.1 Product: -0.25 * -24 Quotient: 3 / 0.5

Answer 1

In mathematics, when rounding rational numbers, you usually round up when the digit to be dropped is 5 or greater, and round down when the digit to be dropped is less than 5. However, if the digit to be dropped is 5 and is followed only by zeros, you round up or down to the nearest even value.

Step-by-step explanation:

A. Sum: 3.5 - 0.5 Difference: 5.5 - 0.5 Product: -2.5 * -2 Quotient: 3 / 0.5
B. Sum: 6.2 + 0.8 Difference: 7 - 1 Product: -1.5 * -4 Quotient: 9 / 1.5
C. Sum: -2 + 8 Difference: -3 - 3 Product: -0.5 * -12 Quotient: -6 / 1
D. Sum: 2/3 + 4/3 Difference: 1.1 - 0.1 Product: -0.25 * -24 Quotient: 3 / 0.5

When rounding rational numbers, you usually round up when the digit to be dropped is 5 or greater, and round down when the digit to be dropped is less than 5. However, if the digit to be dropped is 5 and is followed only by zeros, you round up or down to the nearest even value.

For example, in expression A, the sum is 3.5 - 0.5, and the answer is 3. The digit to be dropped is 0, so we round down. In expression C, the quotient is -6 / 1, and the answer is -6. The digit to be dropped is 0, but it is followed only by zeros, so we round down to an even value.