Question

5 find the greatest sum, difference, product, and quotient using two of the numbers below for each operation. show your work.
$-3\frac{3}{5}$ 2.75 $-18.3$ 6 $-4$ $9\frac{1}{5}$
solution

Explanation:

Step1: Convert to decimals

Convert mixed numbers and fractions to decimals: \(-3\frac{3}{5} = -3.6\), \(9\frac{1}{5}=9.2\). The numbers are: \(-3.6\), \(2.75\), \(-18.3\), \(6\), \(-4\), \(9.2\).

Step2: Find greatest sum

To maximize sum, use two largest positive numbers: \(9.2 + 6 = 15.2\).

Step3: Find greatest difference

Difference is \(a - b\), maximize by largest \(a\) and smallest \(b\) (most negative). Largest \(a = 9.2\), smallest \(b=-18.3\). So \(9.2 - (-18.3)=9.2 + 18.3 = 27.5\).

Step4: Find greatest product

For product, consider signs: positive product from two negatives or two positives. Calculate:

• Two positives: \(9.2\times6 = 55.2\), \(9.2\times2.75 = 25.3\), \(6\times2.75 = 16.5\).
• Two negatives: \((-3.6)\times(-4)=14.4\), \((-3.6)\times(-18.3)=65.88\), \((-4)\times(-18.3)=73.2\). So greatest product is \(73.2\) (from \(-4\) and \(-18.3\)).

Step5: Find greatest quotient

Quotient \(\frac{a}{b}\), positive quotient (same sign) or negative (opposite). For positive, maximize \(\frac{\text{large positive}}{\text{small positive}}\) or \(\frac{\text{large negative}}{\text{small negative}}\).

• Positive: \(\frac{9.2}{2.75}\approx3.345\), \(\frac{9.2}{6}\approx1.533\), \(\frac{6}{2.75}\approx2.182\), \(\frac{-3.6}{-4}=0.9\), \(\frac{-18.3}{-4}=4.575\), \(\frac{-18.3}{-3.6}\approx5.083\). So greatest positive quotient is \(\frac{-18.3}{-3.6}=5.083\) (or \(\frac{18.3}{3.6}\)). Wait, also check \(\frac{9.2}{2.75}\approx3.345\), \(\frac{18.3}{3.6}=5.083\), \(\frac{18.3}{4}=4.575\). Wait, maybe I missed: \(\frac{9.2}{2.75}\approx3.34\), \(\frac{9.2}{6}\approx1.53\), \(\frac{6}{2.75}\approx2.18\). For negative quotient, it will be negative, so smaller than positive. Wait, another way: \(\frac{9.2}{2.75}\approx3.34\), \(\frac{18.3}{3.6}=5.083\), \(\frac{18.3}{4}=4.575\), \(\frac{9.2}{2.75}\approx3.34\). Wait, also \(\frac{9.2}{2.75}\approx3.34\), but \(\frac{18.3}{3.6}=5.083\) (since \(-18.3\) and \(-3.6\) give positive quotient). Wait, maybe better: \(\frac{9.2}{2.75}\approx3.34\), \(\frac{18.3}{3.6}=5.083\), \(\frac{18.3}{4}=4.575\), \(\frac{9.2}{6}\approx1.53\), \(\frac{6}{2.75}\approx2.18\). So greatest quotient is \(\frac{-18.3}{-3.6}=5.083\) (or \(\frac{18.3}{3.6}\)). Wait, but also check \(\frac{9.2}{2.75}\approx3.34\), so \(\frac{18.3}{3.6}=5.083\) is larger. Alternatively, \(\frac{9.2}{2.75}\approx3.34\), \(\frac{18.3}{3.6}=5.083\), so greatest quotient is \(5.083\) (from \(-18.3\) and \(-3.6\)).

Answer:

• Greatest Sum: \(15.2\) (from \(9\frac{1}{5}\) and \(6\))
• Greatest Difference: \(27.5\) (from \(9\frac{1}{5}\) and \(-18.3\))
• Greatest Product: \(73.2\) (from \(-4\) and \(-18.3\))
• Greatest Quotient: \(\approx5.08\) (from \(-18.3\) and \(-3\frac{3}{5}\))