Sharing Tens in Division
Sharing Tens in Division is a Grade 4 math skill that introduces the first step of dividing a two-digit number: sharing the tens digit equally among the divisor groups before addressing the ones. When dividing 48 by 3, you first share 4 tens among 3 groups — each group gets 1 ten with 1 ten leftover. That leftover ten must be ungrouped into 10 ones before the ones digit can be distributed. Taught in Chapter 13: Division of Tens and Ones with Successive Remainders in Eureka Math Grade 4, this step-by-step approach builds the conceptual foundation for the standard long division algorithm.
Key Concepts
When dividing a two digit number, begin by sharing the tens equally among the groups indicated by the divisor. The number of tens each group receives becomes the tens digit of the quotient. Let $T$ be the number of tens in the dividend and $d$ be the divisor. The number of tens in each group is the whole number result of $T \div d$.
Common Questions
What does sharing tens in division mean?
Sharing tens means distributing the tens digit of the dividend equally among the number of groups indicated by the divisor. For example, dividing 48 by 3 starts by sharing 4 tens into 3 groups — each group gets 1 ten with 1 ten left over as a remainder.
What happens to leftover tens in division?
Leftover tens that cannot be distributed equally are regrouped into ones. One remaining ten becomes 10 ones, which are then combined with the ones digit of the dividend to create the new number to divide in the ones step.
How do I begin solving 75 / 5 by sharing tens?
Start by dividing the tens: 7 tens / 5 = 1 ten per group with 2 tens remaining. Regroup the 2 remaining tens as 20 ones and add to the 5 ones digit: 20 + 5 = 25 ones. Then divide 25 ones by 5 to get 5. The full quotient is 15.
Why do we start division with the tens place?
Starting with the largest place value ensures you account for the biggest part of the dividend first. This left-to-right approach mirrors the standard algorithm and ensures remainders from the tens are correctly combined with ones before the final division step.
How does sharing tens connect to the standard long division algorithm?
Sharing tens is the first step in long division: divide the tens digit by the divisor, place the quotient above the tens digit, multiply back, subtract the remainder, and bring down the ones digit. Understanding the concept before the algorithm prevents mechanical errors.
What chapter in Eureka Math Grade 4 covers sharing tens in division?
Chapter 13: Division of Tens and Ones with Successive Remainders in Eureka Math Grade 4 systematically develops multi-digit division, starting with place value concepts like sharing tens and building toward the full long division algorithm.