Question

1. jeanne will use more than \\(\frac{2}{4}\\) cup of sugar but less than 1 cup of sugar for a recipe. which benchmark fraction of a cup does jeanne use?\

\\(\boldsymbol{\text{ⓐ } \frac{1}{2}}\\)\
\\(\boldsymbol{\text{ⓑ } 1}\\)\
\\(\boldsymbol{\text{ⓒ } \frac{1}{4}}\\)\
\\(\boldsymbol{\text{ⓓ } \frac{3}{4}}\\)\

1. a. estimate \\(55 \div 7\\).\

b. what is the remainder of \\(55 \div 7\\)?

Explanation:

Question 16

Step1: Simplify \(\frac{2}{4}\)

Simplify \(\frac{2}{4}\) to \(\frac{1}{2}\) (since dividing numerator and denominator by 2 gives \(\frac{2\div2}{4\div2}=\frac{1}{2}\)). So Jeanne uses more than \(\frac{1}{2}\) cup (because \(\frac{2}{4}=\frac{1}{2}\)) and less than 1 cup.

Step2: Analyze each option

• Option A: \(\frac{1}{2}\) is equal to \(\frac{2}{4}\), but Jeanne uses more than \(\frac{2}{4}\), so A is incorrect.
• Option B: 1 cup is not less than 1 cup, so B is incorrect.
• Option C: \(\frac{1}{4}\) is less than \(\frac{2}{4}\), so C is incorrect.
• Option D: \(\frac{3}{4}\) is more than \(\frac{2}{4}\) (since \(\frac{3}{4}>\frac{2}{4}\)) and less than 1 (since \(\frac{3}{4}<1\)), so D is correct.

Step1: Find a multiple of 7 close to 55

We know that \(7\times7 = 49\) and \(7\times8=56\). 55 is closer to 49 or 56? 55 - 49 = 6, 56 - 55 = 1. Wait, actually, when estimating division, we can think of a number that 7 multiplies to get close to 55. Since \(7\times8 = 56\) which is very close to 55 (only 1 more), so we can estimate \(55\div7\approx8\) (or alternatively, since \(7\times7 = 49\), and 55 - 49 = 6, so it's about 7 + \(\frac{6}{7}\approx7.86\), but a common estimate is 8 or 7.8 - 8). Another way: 7*8=56, so 55÷7≈8 (because 56 is very close to 55, so we can say the estimate is 8, or sometimes 7.8 is approximated to 8 or 7 - 8).

Step2: Confirm the estimate

Since 77=49 and 78=56, 55 is 1 less than 56, so \(55\div7\) is approximately 8 (because 56÷7=8, so 55÷7≈8).

Step1: Divide 55 by 7

We know that \(7\times7 = 49\). Now, subtract 49 from 55: \(55 - 49=6\). The remainder is the amount left after dividing as much as possible. So when we divide 55 by 7, 7 goes into 55 seven times (7*7=49) with a remainder of \(55 - 49 = 6\).

Step2: Check the remainder rule

The remainder must be less than the divisor (7). Since 6 < 7, the remainder is 6.

Answer:

D. \(\frac{3}{4}\)

Question 17 A