Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 975 \div 6 = 162.5 \)
\( 478 \times 38 = 18{,}164 \)
Solution
Sure, let's solve each of the problems step by step.
### Problem (5): \( 975 \div 6 \)
To divide 975 by 6:
1. **Calculate the quotient:**
\[
975 \div 6 = 162.5
\]
- **Explanation:**
- \(6 \times 162 = 972\)
- \(975 - 972 = 3\)
- The remainder is 3, which is \(\frac{3}{6} = 0.5\)
- So, \(162 + 0.5 = 162.5\)
### Problem: \( 478 \times 38 \)
To multiply 478 by 38:
1. **Breakdown the multiplication:**
\[
478 \times 38 = (400 + 70 + 8) \times 38
\]
2. **Calculate each part:**
\[
400 \times 38 = 15{,}200
\]
\[
70 \times 38 = 2{,}660
\]
\[
8 \times 38 = 304
\]
3. **Add them together:**
\[
15{,}200 + 2{,}660 + 304 = 18{,}164
\]
- **Alternatively, using standard multiplication:**
\[
\begin{array}{r}
\phantom{0}478 \\
\times\phantom{0}38 \\
\hline
3{,}824 \quad (\text{478} \times 8) \\
+14{,}340 \quad (\text{478} \times 30) \\
\hline
18{,}164 \\
\end{array}
\]
### **Final Answers:**
\[
\begin{aligned}
(5)\quad 975 \div 6 &= 162.5 \\
478 \times 38 &= 18{,}164 \\
\end{aligned}
\]
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Simplify this solution The Deep Dive
To tackle \( 975 \div 6 \), you could break it down by estimating first; since 6 goes into 975 roughly 162 times. When you divide, you'll get \( 162.5 \) as the precise answer. Isn't division neat? It’s like sharing equally, just make sure your numbers get along! As for \( 478 \times 38 \), this multiplication can seem daunting, but think of it as combining different parts! You can split 38 into 30 and 8. By multiplying separately (i.e., \( 478 \times 30 \) gives you 14,340 and \( 478 \times 8 \) gives 3,824), and adding them up will reveal \( 18,164 \). Multiplication can remind us of teamwork; every number plays a vital role!
