Q. What are 2 ways to simplify \(4.5 + 312.4 + 1.7\)?
Answer
Method 1: \( (4.5+1.7)+312.4 = 6.2+312.4 = 318.6.\)
Method 2: \( 4.5+(312.4+1.7) = 4.5+314.1 = 318.6.\)
Detailed Explanation
Problem
Simplify the expression \(\;4.5 + 312.4 + 1.7\;\).
Method 1 — Use the associative/commutative properties to group convenient terms
- We may change the order and grouping of addition without changing the result. Choose to add the two smaller decimals first: \(\;(4.5 + 1.7) + 312.4\;.\)
- Compute the sum inside the parentheses. Align decimal places or add tenths directly: the tenths parts are 0.5 and 0.7, which sum to 1.2, so
\(\;4.5 + 1.7 = 6.2\;.\) - Now add that result to 312.4:
\(\;6.2 + 312.4 = 318.6\;.\) - Conclusion: \(\;4.5 + 312.4 + 1.7 = 318.6\;.\)
Method 2 — Convert to tenths (fractions) and add exactly
- Write each decimal as a fraction with denominator 10:
\(\;4.5 = \dfrac{45}{10},\quad 312.4 = \dfrac{3124}{10},\quad 1.7 = \dfrac{17}{10}\;.\) - Add the fractions (common denominator 10):
\(\;\dfrac{45}{10} + \dfrac{3124}{10} + \dfrac{17}{10} = \dfrac{45 + 3124 + 17}{10}\;.\) - Compute the numerator:
\(\;45 + 3124 + 17 = 3186\;,\) so the sum is \(\;\dfrac{3186}{10}\;.\) - Convert back to a decimal by dividing by 10:
\(\;\dfrac{3186}{10} = 318.6\;.\) - Conclusion: \(\;4.5 + 312.4 + 1.7 = 318.6\;.\)
See full solution
Arithmetic FAQs
What are two quick ways to simplify \(4.5+312.4+1.7\)?.
Pair the decimals: \( (4.5+1.7)+312.4=6.2+312.4=318.6 \). Or scale to integers: multiply by 10, add \(45+3124+17=3186\), then divide by 10 to get \(318.6\).
Why can I add in a different order?
Because addition is commutative and associative: you may reorder and regroup terms. For any numbers \(a,b,c\), \(a+b+c=(a+c)+b=(b+a)+c\). This lets you pair convenient sums.
How do I check my answer quickly?
Recompute with a different grouping: add \(312.4+4.5=316.9\) then \(316.9+1.7=318.6\). Or use the integer scaling method: \(3186\div10=318.6\). Matching results confirms correctness.
Can I round first to estimate?
Yes. Estimate \(4.5+1.7\approx6.2\) and \(312.4\approx312\), so \(312+6.2\approx318.2\). For better estimate round \(312.4\) to \(312.4\); exact is \(318.6\). Use adjustment after rounding for accuracy.
How would I do this with column addition?
Align decimal points and add vertically:
\[
\begin{array}{r}
312.4\\
+\, 4.5\\
+\, 1.7\\
\hline
318.6\\
\end{array}
\]
This avoids regrouping mistakes and is systematic..
Could I convert to fractions instead?.
Could I convert to fractions instead?.
Any mental-math tips for decimals?
Pair numbers that make whole or simple decimals (e.g., \(4.5+1.7=6.2\)). Scale by powers of 10 to remove decimals, add integers, then rescale. Keep decimal points aligned when adding mentally.
What is the exact final result?
The exact sum is \(318.6\).
Learn two ways to simplify decimals
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