Q1: How do you solve division problems?
Ans: To solve division problems, we read the problem and identify the dividend and the divisor. Then, we divide the dividend by the divisor either mentally or by using long division method. We may also need to solve the problem further to get to the final answer.
Q2: What is a division fact for 5th Graders?
Ans: Division facts are the division number sentences related to times tables. Therefore: 30 ÷ 3 = 10, 27 ÷ 3 = 9 and 24 ÷ 3 = 8 are all division facts for the three times table. By year 5, children know all of their times tables up to 12 x 12, and the corresponding division facts. They use the division facts to solve division problems involving larger numbers.
Q3: How do you divide numbers using long division?
Ans: To divide numbers using long division, we put the divisor outside the division box and dividend inside it. We identify the first one or two digits that are closest to multiple of divisor which is either equal or less than first one or two digits. We write the multiple in quotient box and below the digits in the dividend. Then, we subtract the multiple of divisor from first digits of the dividend. Then answer obtained is the remainder in this case. We bring down the next digit of dividend and repeat the same process till we obtain the final remainder which is either 0 or a number less than the divisor.
The previous grade fosters reasoning skills in kids to derive an arithmetic expression from the given word problem. With suitable operators to swiftly add, subtract, multiply and divide 4-digit numbers by a single-digit number; the result of “division” operation is computed in terms of quotient and remainder. Also, long division methods and division by multiples of 10 and 100 enable to quickly divide the numbers and obtain a precise answer.
In grade 5, the 2-digit divisors are introduced to further enhance the skills for advanced math. Understanding of concepts like know-how technique to form multiplication tables; kids assimilate the proficiency in the estimation of the divisor and dividend to the nearest multiple of 10. The technique boosts fast math skills and enables kids to estimate the quotients as well. The apprehension of “division” to fractional numbers and place value system is instrumental in learning measurements and cognate the conversion techniques.
“Division” as a math technique for the 5th graders is narrated as:
“Formulation of a fair sharing model to divide the number (dividend) in the specified number of groups (divisor)”.
For example:
The abstract knowledge of foundational math skills is enhanced in each grade to learn the applicability and practical aspects. “Division” as a math essential begins by creating a partition model to conceptualize and associated it with visual observation. Fun learning math games for SplashLearn further hones the proficiency in dividing 4-digit numbers by a single-digit number and computing the quotient and the remainder (if any). Easy-to-grasp math games aligned to common core math standards for grade-5 extend the skill to the division of numbers involving fractions and double-digit divisors.
Well-formulated games assist kids to excel in math and engage in efficient homeschooling.
In the 5th grade, reasoning to comprehend a word problem is nurtured by formulating valid expressions. Kids learn to use standard algorithms and the corresponding properties of the math operations (such as the distributive property of multiplication; as a x b = b x a). With the knowledge of the base-10 system and estimating the closest multiple of 10 corresponding to a number; kids learn to strategically break the dividend and the divisor apart in base-10 units for estimating the quotient.
Projected learning outcomes are listed as follows:
To learn the “division” operation involving fractions and 2-digit division, required math essentials insist fluently solving single-step and multistep math operations. These operations are addition, subtraction, multiplication, and division of 4-digit numbers. The significant command in multiplying double-digit number to the single-digit number for close estimation is helpful in working on long division method.
Comprehension of the place-value system along with the interpretation in base-10 blocks and unit blocks are instrumental in the cultivation of visual observation skills to divide by fractional divisors.
SplashLearn worksheets encourage kids to think logically with reasoning and language comprehension to understand math concepts. Unique, engaging and interactive interface with a colorful theme-based display foster deep-rooted concepts in kids. Following a well-planned routine to solve the comprehensive exercises assists in fast mental calculations and excel in math without any fear.
The upcoming section discusses the different cases with 2-digit numbers & fractional values as the divisor and corresponding decimal arithmetic.
To divide a number (between 10 and 10,000) by a 2-digit divisor (between 10 and 99), the long division method is followed. Two possible answers in such division are either whole number as a quotient or a quotient with a remainder. The remainder will always be less than the divisor.
To divide a number by a two-digit divisor, consider an example as follows:
– 25↓ _ →25 x 1 = 25
175
– 175 → 25 x 7 = 175
000 → No Remainder
To solve the problem using fast math skills, estimate the closest value (a multiple of 10s and closer to the dividend) which upon subtraction will yield 0 or a remainder less than the divisor. For example,
As discussed previously, the division result may end in a quotient and a remainder. Consider the following example:
– 66↓ _ →22 x 3 = 66
078
– 066 → 22 x 3 = 66
012 → Remainder
– 60↓ _ →20 x 3 = 60
100
– 100 → 20 x 5 = 100
000 → No Remainder
As kids learn the division techniques for whole numbers and dividing the number by a multi-digit divisor (single digit and two-digit), learning the “division” by fractional values turns easy.
Following chart illustrates the multiple cases of the division with unit fractional values.
To divide a unit fraction by a whole number, illustration similar to a line plot is helpful in understanding the method.
÷ 3 ➔ X 
➔ 
➔ 
Reference image: To divide 1/7 by 3, divide 1/7 into 3 blocks each.
As the numbers are interchanged, a case in which a dividend is a whole number and the divisor is a unit fraction, the “division” equation is similarly framed using the line plot. The only difference is in the numerator instead of the denominator.
➔ 3 X 
➔ 
➔ 
➔ 15
Reference image: To divide 3 by 1/5, count the number of blocks
The previous section illustrates the division of unit fractions by whole numbers and whole numbers by unit fractions. In decimal arithmetic, the division is performed by representing the decimal values in a fractional form with the denominator as a multiple of 10. The denominator is evaluated by the place value of decimal.
Following chart illustrates some examples of division problems involving decimal arithmetic.
To divide a decimal number by a multiple of 10, adjustment in the place value of decimal is the first step. The decimal is adjusted to the left by one place with each 10.
To divide a decimal number by a whole number, place value system to rewrite a decimal number is helpful in framing an easy division equation. Following the method of long division or short division as per the multi-digit divisor, an equation can be solved as illustrated in the example.
To divide a decimal number by another decimal number, division equations are framed with the knowledge of place value system and cancellation of base 10 multiples with each other. The concept is illustrated with an example for understanding the technique.
“Division” operation using decimal arithmetic, unit fractions, and the multi-digit divisor is the foundation of learning measurement, data representation, and geometry. Also, in practical aspects, the concept is used widely for drawing maps, re-scaling measurements such as length and height proportionately, converting physical quantities like weight and capacity etc. to different units (metric and US customary) for easy interpretation.
The utility of basic math operations in learning advanced math concepts is evident from the complexity of word problems in grade-5. With the development of division skills to fractional and 2-digit divisors; kids understand and grasp the math involved in data representation, measurement and geometry and comprehension of “fair sharing model”.
Also, day-to-day math problems, strengthen the reasoning skill in kids. SplashLearn worksheets on “division”, comprising of puzzles, math riddles, single-step and multistep word problems are an ideal summer-vacation assistant to prevent the skill loss. Neatly planned pre-k curriculum garnered special appreciation from mentors engaged in home schooling. Start practicing the exciting math games today to boost confidence and excel in math.
