Question

use multiplication and division facts to solve the following problems mentally. remember: write an equivalent name for the dividend by breaking it into smaller parts that are easier to divide. example: 72 divided by 4 - write some multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 - write an equivalent name by breaking 72 into smaller numbers that are multiples of 4. equivalent name for 72: 40 + 32 - use the equivalent name to divide mentally. ask yourself: how many 4s are in 40? (10) how many 4s are in 32? (8) think: how many total 4s are in 72? (10 4s + 8 4s = 18 4s, so 72 ÷ 4 = 18) ① 57 ÷ 3 →? multiples of 3: ___________ equivalent name for 57: _________ 57 ÷ 3 → ____ ② 96 ÷ 8 →? multiples of 8: _________ equivalent name for 96: _________ 96 ÷ 8 → ____ practice make an estimate and solve. ③ 68 23 estimate: ____ ④ 278 15 estimate: ______

Explanation:

Problem ①: \( 57 \div 3 \)

Step1: List multiples of 3

Multiples of 3: \( 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57 \) (we can pick two that add to 57, e.g., \( 30 + 27 \))

Step2: Equivalent name for 57

Equivalent name for 57: \( 30 + 27 \)

Step3: Divide each part by 3

\( 30 \div 3 = 10 \), \( 27 \div 3 = 9 \)

Step4: Sum the results

\( 10 + 9 = 19 \)

Step1: List multiples of 8

Multiples of 8: \( 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 \) (we can pick two that add to 96, e.g., \( 80 + 16 \))

Step2: Equivalent name for 96

Equivalent name for 96: \( 80 + 16 \)

Step3: Divide each part by 8

\( 80 \div 8 = 10 \), \( 16 \div 8 = 2 \)

Step4: Sum the results

\( 10 + 2 = 12 \)

Step1: Estimate

Round 68 to 70 and 23 to 20. Estimate: \( 70 \times 20 = 1400 \)

Step2: Solve using multiplication

\( 68 \times 23 = 68 \times (20 + 3) = 68 \times 20 + 68 \times 3 = 1360 + 204 = 1564 \)

Answer:

\( 19 \)

Problem ②: \( 96 \div 8 \)