Question

1. consider $590 \div 6$

a. estimate the quotient.
b. draw a diagram or use the partial quotients method to find the quotient.

1. consider $254 \div 21$

a. estimate the quotient.
b. draw a diagram or use partial quotients to find the quotient.

Explanation:

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Problem 1: $590 \div 6$

Step1: Round values for estimation

Round 590 to 600 (a multiple of 6).
$\frac{600}{6}=100$

Step2: Partial quotients method, first chunk

Subtract $6\times90=540$ from 590.
$590 - 540 = 50$

Step3: Partial quotients method, second chunk

Subtract $6\times8=48$ from 50.
$50 - 48 = 2$

Step4: Sum partial quotients

Add 90 and 8, remainder 2.
$90 + 8 = 98$
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Problem 2: $254 \div 21$

Step1: Round values for estimation

Round 254 to 240, 21 to 20 (easy multiples).
$\frac{240}{20}=12$

Step2: Partial quotients method, first chunk

Subtract $21\times10=210$ from 254.
$254 - 210 = 44$

Step3: Partial quotients method, second chunk

Subtract $21\times2=42$ from 44.
$44 - 42 = 2$

Step4: Sum partial quotients

Add 10 and 2, remainder 2.
$10 + 2 = 12$
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Answer:

1. a. Estimated quotient: $100$

b. Exact quotient: $98$ with a remainder of $2$

1. a. Estimated quotient: $12$

b. Exact quotient: $12$ with a remainder of $2$