Question

find each quotient. use the space
a. 688 ÷ 7 =

d. 206 ÷ 4 =

g. 377 ÷ 4 =

Explanation:

Part a: \( 688 \div 7 \)

Step 1: Divide 688 by 7

We know that \( 7\times98 = 686 \), and \( 688 - 686=2 \). So \( 688\div7=\frac{688}{7}=98\frac{2}{7}\approx98.29 \) (if we want a decimal approximation) or as a mixed number \( 98\frac{2}{7} \). But usually, for such division, we can present the quotient and remainder. The quotient is 98 and the remainder is 2. So \( 688\div7 = 98\) with a remainder of 2, or as a decimal \( \approx98.29 \) (rounded to two decimal places).

Step 2: Final result

If we consider the quotient with remainder, it's \( 98\) R \( 2 \), and as a decimal (approximate) it's \( 98.29 \) (or more precisely \( 98.\overline{285714} \) since \( \frac{2}{7}=0.\overline{285714} \)). But if we do the division:
\( 7\) into \( 68 \) (the first two digits of 688) is \( 9\) (since \( 7\times9 = 63 \), \( 68 - 63 = 5 \)). Bring down the 8 to make 58. \( 7\) into \( 58 \) is \( 8\) ( \( 7\times8 = 56 \), \( 58 - 56 = 2 \)). Bring down the last 8 to make 28? Wait, no, wait, the number is 688. Wait, my mistake earlier. Let's do long division properly.

Long division for \( 688\div7 \):

• 7 goes into 6 zero times.
• 7 goes into 68 nine times (\( 7\times9 = 63 \)), subtract \( 63 \) from \( 68 \), we get \( 5 \).
• Bring down the 8 to make \( 58 \).
• 7 goes into \( 58 \) eight times (\( 7\times8 = 56 \)), subtract \( 56 \) from \( 58 \), we get \( 2 \).
• Bring down the last 8? Wait, no, 688 is a three - digit number. Wait, 6 (hundreds place), 8 (tens place), 8 (units place). So after dividing 68 (tens and hundreds) by 7, we had a remainder of 5, then we bring down the 8 (units place) to make 58 (tens and units). After dividing 58 by 7 (8 times, remainder 2), there are no more digits to bring down. So the quotient is 98 (9 in tens place, 8 in units place) and the remainder is 2. So \( 688\div7 = 98\) R \( 2 \), and as a decimal \( 98+\frac{2}{7}\approx98.29 \)

Part d: \( 206\div4 \)

Step 1: Divide 206 by 4

We know that \( 4\times51 = 204 \), and \( 206 - 204 = 2 \). So \( 206\div4=\frac{206}{4}=51\frac{2}{4}=51\frac{1}{2}=51.5 \)

Step 2: Final result

So \( 206\div4 = 51.5 \) (or as a mixed number \( 51\frac{1}{2} \))

Part g: \( 377\div4 \)

Step 1: Divide 377 by 4

We know that \( 4\times94 = 376 \), and \( 377 - 376 = 1 \). So \( 377\div4=\frac{377}{4}=94\frac{1}{4}=94.25 \)

Step 2: Final result

So \( 377\div4 = 94.25 \) (or as a mixed number \( 94\frac{1}{4} \))

Answer:

s:
a. \( 688\div7 = 98\) R \( 2 \) (or \( 98\frac{2}{7}\approx98.29 \))
d. \( 206\div4 = 51.5 \)
g. \( 377\div4 = 94.25 \)