Question

adding positive and negative fractions and decimals
circle all the problems that will have a negative sum. then find the sum of only the problems you circled.
1 $4\frac{1}{2}+6\frac{1}{4}$ 2 $-2\frac{2}{3}+1\frac{1}{6}$ 3 $-\frac{2}{3}+\frac{7}{8}$
4 $-4.3 + 1.4$ 5 $-12.04+( - 3.6)$ 6 $15.37+( - 15.28)$
7 $-2\frac{2}{3}+( - 3\frac{3}{4})$ 8 $5+( - 7\frac{3}{5})$ 9 $-3.18 + 8.02$
$-6\frac{2}{7}+3\frac{1}{14}$ 11 $-3.8 + 7.2$ 12 $-4.7+( - 5\frac{13}{20})$
$-18\frac{1}{2}+27\frac{3}{5}$ 14 $-12+4\frac{3}{5}$ 15 $-7\frac{3}{5}+( - 3\frac{2}{3})$
without performing the addition, how can you determine when the sum of two numbers will be negative?

Explanation:

Step1: Convert mixed numbers to improper fractions or decimals

• For \( -2\frac{2}{3}+1\frac{1}{6}\):

\(-2\frac{2}{3}=-\frac{8}{3}=-\frac{16}{6}\), \(1\frac{1}{6}=\frac{7}{6}\)

• For \( -4.3 + 1.4\):

Keep as decimals.

• For \( -12.04+( - 3.6)\):

Keep as decimals.

• For \( -2\frac{2}{3}+(-3\frac{3}{4})\):

\(-2\frac{2}{3}=-\frac{8}{3}=-\frac{32}{12}\), \(-3\frac{3}{4}=-\frac{15}{4}=-\frac{45}{12}\)

• For \(5+( - 7\frac{3}{5})\):

\(-7\frac{3}{5}=-\frac{38}{5}\), \(5=\frac{25}{5}\)

• For \( - 6\frac{2}{7}+3\frac{1}{14}\):

\(-6\frac{2}{7}=-\frac{44}{7}=-\frac{88}{14}\), \(3\frac{1}{14}=\frac{43}{14}\)

• For \( - 12 + 4\frac{3}{5}\):

\(4\frac{3}{5}=\frac{23}{5}=4.6\)

• For \( - 7\frac{3}{5}+(-3\frac{2}{3})\):

\(-7\frac{3}{5}=-\frac{38}{5}=-\frac{114}{15}\), \(-3\frac{2}{3}=-\frac{11}{3}=-\frac{55}{15}\)

Step2: Calculate each sum

• \( -2\frac{2}{3}+1\frac{1}{6}=-\frac{16}{6}+\frac{7}{6}=-\frac{9}{6}=-\frac{3}{2}=-1.5\)
• \( -4.3 + 1.4=-2.9\)
• \( -12.04+( - 3.6)=-12.04 - 3.6=-15.64\)
• \( -2\frac{2}{3}+(-3\frac{3}{4})=-\frac{32}{12}-\frac{45}{12}=-\frac{77}{12}\approx - 6.42\)
• \(5+( - 7\frac{3}{5})=\frac{25}{5}-\frac{38}{5}=-\frac{13}{5}=-2.6\)
• \( - 6\frac{2}{7}+3\frac{1}{14}=-\frac{88}{14}+\frac{43}{14}=-\frac{45}{14}\approx - 3.21\)
• \( - 12 + 4\frac{3}{5}=-12 + 4.6=-7.4\)
• \( - 7\frac{3}{5}+(-3\frac{2}{3})=-\frac{114}{15}-\frac{55}{15}=-\frac{169}{15}\approx - 11.27\)

Step3: Sum the negative - sum problems

\(-1.5+( - 2.9)+(-15.64)+(-6.42)+(-2.6)+(-3.21)+(-7.4)+(-11.27)\)
\(=-(1.5 + 2.9+15.64+6.42+2.6+3.21+7.4+11.27)\)
\(=-(1.5+2.9)+(-15.64+(-6.42))+(-2.6+(-3.21))+(-7.4+(-11.27))\)
\(=-4.4-22.06-5.81-18.67\)
\(=-(4.4 + 22.06+5.81+18.67)\)
\(=-50.94\)

Answer:

The sum of the problems with negative sums is \(-50.94\)