Divide 899 loaves of bread among 27 homeless shelters.

Mathematics
Divide 899 loaves of bread among 27 homeless shelters.

ScanSolve AI Answer

Answer

43 remainder 6

Step 1: Which estimate was closer to the actual? Give a reason.

The estimates are 90030=30\frac{900}{30} = 30 and 100030≈33\frac{1000}{30} \approx 33.

Actual: 27×36=97227 \times 36 = 972, 979−972=7979 - 972 = 7, so quotient 3636, remainder 77.

27×36:20×36=720,7×36=252,720+252=972.\begin{align*} &27 \times 36: \\ &20 \times 36 = 720, \\ &7 \times 36 = 252, \\ &720 + 252 = 972. \end{align*}

3333 is closer to 3636 (∣36−33∣=3|36-33|=3) than 3030 (∣36−30∣=6|36-30|=6).

Reason: 979979 is closer to 10001000 (2121 away) than to 900900 (7979 away).

Step 2a: 350÷8350 \div 8

Test 44×844 \times 8:

44×8=40×8+4×8=320+32=352>350.44 \times 8 = 40 \times 8 + 4 \times 8 = 320 + 32 = 352 > 350.

Test 43×843 \times 8:

8×43:8×40=320,8×3=24,320+24=344,350−344=6.\begin{align*} &8 \times 43: \\ &8 \times 40 = 320, \\ &8 \times 3 = 24, \\ &320 + 24 = 344, \\ &350 - 344 = 6. \end{align*}

350=8×43+6350 = 8 \times 43 + 6.

43 remainder 6

Step 2b: 4300÷44300 \div 4

4×1000=4000,4 \times 1000 = 4000, 4300−4000=300.4300 - 4000 = 300. 4×75=300,4 \times 75 = 300, 1000+75=1075,1000 + 75 = 1075, 4300−4×1075=0.4300 - 4 \times 1075 = 0.

4300=4×1075+04300 = 4 \times 1075 + 0.

1075

Step 2c: 7436÷67436 \div 6

6×1200=7200,6 \times 1200 = 7200, 7436−7200=236.7436 - 7200 = 236. 6×39=234,6 \times 39 = 234, 7200+234=7434,7200 + 234 = 7434, 7436−7434=2.7436 - 7434 = 2.

7436=6×1239+27436 = 6 \times 1239 + 2.

1239 remainder 2

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Quick Answer

Which estimate was closer to the actual? Give a reason. The estimates are (900)/(30) = 30 and (1000)/(30) ≈ 33.

Divide 899 loaves of bread among 27 homeless shelters.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Which estimate was closer to the actual? Give a reason. The estimates are (900)/(30) = 30 and (1000)/(30) ≈ 33. Actual: 27 × 36 = 972, 979 - 972 = 7, so quotient 36, remainder 7. &27 × 36: \\ &20 × 36 = 720, \\ &7 × 36 = 252, \\ &720 + 252 = 972. 33 is closer to 36 (|36-33|=3) than 30 (|36-30|=6). Reason: 979 is closer to 1000 (21 away) than to 900 (79 away). Step 2a: 350 ÷ 8 Test 44 × 8: 44 × 8 = 40 × 8 + 4 × 8 = 320 + 32 = 352 > 350. Test 43 × 8: &8 × 43: \\ &8 × 40 = 320, \\ &8 × 3 = 24, \\ &320 + 24 = 344, \\ &350 - 344 = 6. 350 = 8 × 43 + 6. 43 remainder 6 Step 2b: 4300 ÷ 4 4 × 1000 = 4000, 4300 - 4000 = 300. 4 × 75 = 300, 1000 + 75 = 1075, 4300 - 4 × 1075 = 0. 4300 = 4 × 1075 + 0. 1075 Step 2c: 7436 ÷ 6 6 × 1200 = 7200, 7436 - 7200 = 236. 6 × 39 = 234, 7200 + 234 = 7434, 7436 - 7434 = 2. 7436 = 6 × 1239 + 2. 1239 remainder 2