Sensim Math Original · sm-1
SM Original Grade 5 arithmeticProblem
A baker writes the total amount of flour (in kilograms) for one large batch as a sum of three fractions. What is the value of this expression in decimal form?
972+3075+70063
Pick an answer.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: A baker has written the total flour for a big batch as $\frac{72}{9} + \frac{75}{30} + \frac{63}{700}$ (in kilograms). We need to find this value as a decimal and match it to one of the five answer choices.
Givens: A sum of three fractions: $\frac{72}{9} + \frac{75}{30} + \frac{63}{700}$; Each fraction has a clean common factor (9, 15, and 7 respectively), so each term reduces to a simple decimal; Five answer choices: (A) 10.09, (B) 10.509, (C) 10.59, (D) 10.9, (E) 10.95
Unknowns: The decimal value of the entire sum
Understand
Restated: A baker has written the total flour for a big batch as $\frac{72}{9} + \frac{75}{30} + \frac{63}{700}$ (in kilograms). We need to find this value as a decimal and match it to one of the five answer choices.
Givens: A sum of three fractions: $\frac{72}{9} + \frac{75}{30} + \frac{63}{700}$; Each fraction has a clean common factor (9, 15, and 7 respectively), so each term reduces to a simple decimal; Five answer choices: (A) 10.09, (B) 10.509, (C) 10.59, (D) 10.9, (E) 10.95
Plan
Primary tool: #7 Identify Subproblems
Secondary: #3 Eliminate Possibilities
Trying to add the three fractions with a common denominator at once (e.g. $6300$) gives messy multi-digit arithmetic. Instead we **split the sum into three independent subproblems** (Tool #7): convert each fraction to a decimal on its own, then add. Every sub-piece is small enough for mental arithmetic. Since the problem is multiple-choice, we close with **Tool #3 (Eliminate Possibilities)** to confirm our value against the five offered decimals.
Execute — Answer: C
3.OA.C.7 Step 1 - Handle the first term $\frac{72}{9}$.
- Because $72 = 9 \times 8$, the division comes out exactly and the fraction equals the whole number $8$.
💡 Fluency with multiplication and division within 100 is a Grade 3 standard, so $72 \div 9$ is immediate.
4.NF.A.1 Step 2 - Handle the second term $\frac{75}{30}$.
- Dividing numerator and denominator both by $15$ gives the equivalent fraction $\frac{5}{2}$.
- (You can also do it in two steps: divide by $5$ to get $\frac{15}{6}$, then by $3$ to reach $\frac{5}{2}$.)
💡 Dividing the numerator and denominator by a common factor to get an equivalent fraction is taught in Grade 4.
5.NF.B.3 Step 3 - Convert the simplified $\frac{5}{2}$ to a decimal.
- A fraction means "numerator divided by denominator," so $5 \div 2 = 2.5$.
💡 Interpreting a fraction as numerator-divided-by-denominator and writing it as a decimal is the heart of Grade 5 fractions.
4.NF.C.6 Step 4 - Handle the third term $\frac{63}{700}$.
- Dividing top and bottom by $7$ gives $\frac{9}{100}$.
- A fraction with denominator $100$ translates directly into two decimal places, so the value is $0.09$.
💡 Rewriting a fraction with denominator $10$ or $100$ in decimal notation is exactly the Grade 4 fraction-to-decimal standard.
5.NBT.B.7 Step 5 - Finally, add the three decimals, lining up the decimal points.
- The ones column gives $8+2=10$ (with a carry), the tenths column gives $0+5+0=5$, and the hundredths column gives $0+0+9=9$, so the sum is $10.59$.
💡 Adding decimals to hundredths is a Grade 5 standard; once the place values are aligned it behaves just like whole-number addition.
5.NBT.A.3 Step 6 - Cross-check against the answer choices.
- The candidates are $10.09$, $10.509$, $10.59$, $10.9$, and $10.95$.
- Our computed value $10.59$ matches choice **(C)** exactly.
- (A) $10.09$ drops the $2.5$ tenths from the second term; (B) $10.509$ has a thousandths digit our calculation never produces; (D) $10.9$ ignores the small $0.09$ piece; (E) $10.95$ has the tenths and hundredths digits swapped.
💡 Reading and comparing decimals to thousandths place-by-place is the Grade 5 standard that makes the elimination safe.
3.OA.C.7 Handle the first term $\frac{72}{9}$. Because $72 = 9 \times 8$, the division co 4.NF.A.1 Handle the second term $\frac{75}{30}$. Dividing numerator and denominator both 5.NF.B.3 Convert the simplified $\frac{5}{2}$ to a decimal. A fraction means "numerator d 4.NF.C.6 Handle the third term $\frac{63}{700}$. Dividing top and bottom by $7$ gives $\f 5.NBT.B.7 Finally, add the three decimals, lining up the decimal points. The ones column g 5.NBT.A.3 Cross-check against the answer choices. The candidates are $10.09$, $10.509$, $1 Review
Reasonableness: Quick magnitude check: the first term is $8$, the second is between $2$ and $3$, and the third is a tiny number close to $0$, so the sum should land near $8 + 2.5 + 0 \approx 10.5$. The value $10.59$ sits exactly where we expect, with the small extra $0.09$ from the third term accounted for. Choices like $10.9$ ignore the hundredths digit, $10.95$ has the digits flipped, $10.09$ throws away the $2.5$ entirely, and $10.509$ has a thousandths digit that our calculation cannot produce.
Alternative: An alternative is Tool #13 (Convert to Algebra): give all three fractions a common denominator of $6300$, add the numerators, then convert. $\frac{50400}{6300} + \frac{15750}{6300} + \frac{567}{6300} = \frac{66717}{6300} = 10.59$. The answer is the same, but the arithmetic is heavier, so splitting term-by-term with Tool #7 is the friendlier path for an elementary student.
CCSS standards used (min grade 5)
3.OA.C.7Fluently multiply and divide within 100 (Computing $72 \div 9 = 8$ in one step.)4.NF.A.1Explain why a fraction is equivalent to another fraction (Reducing $\frac{75}{30}$ to the equivalent fraction $\frac{5}{2}$ by dividing numerator and denominator by $15$.)4.NF.C.6Use decimal notation for fractions with denominators 10 or 100 (Rewriting $\frac{9}{100}$ as the decimal $0.09$.)5.NF.B.3Interpret a fraction as division of the numerator by the denominator (Converting $\frac{5}{2}$ to the decimal $2.5$ via $5 \div 2$.)5.NBT.A.3Read, write, and compare decimals to thousandths (Comparing the computed value to the five decimal answer choices $10.09$, $10.509$, $10.59$, $10.9$, $10.95$ digit by digit.)5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths (Performing the final aligned-decimal addition $8 + 2.5 + 0.09 = 10.59$.)
⭐ This problem only needs Grade 5 fraction-to-decimal conversion and decimal addition you already know!
⭐ This problem only needs Grade 5 fraction-to-decimal conversion and decimal addition you already know!
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