Common misconceptions › Class 6 › Maths › Fractions Class 6 Maths · Chapter 7 · NCERT (fegp107)
Fractions: common misconceptions
See the tempting mistake students make in Fractions, why it feels right at first glance, and a worked visual example that shows the right idea.
Worked visual (2) “If your child says…” (8) Teach & practice 2 worked misconception examples Worked example 1 of 2
Can you add the bottom numbers? Wrong
1/2 + 1/3 = 2/5
Why it feels right. I use the whole-number rule for adding on both rows. One plus one is two. Two plus three is five.
Right
Add equal-sized parts. Here 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Worked example
1/2 1/3 2/5 5/6 The proposed 2/5 is shorter than the 1/2 you started with. The sum fills five sixths. Split both bars into sixths. The half fills 3 sixths and the third fills 2 sixths. Together they fill 5 sixths. The proposed 2/5 is smaller than 1/2, even though we added a positive amount to 1/2. Worked example 2 of 2
Can adding one to both numbers keep a fraction equal? Wrong
2/3 = 3/4
Why it feels right. I add one to both numbers and expect the changes to cancel out, like doing the same thing to both sides of an equation.
Right
Multiply or divide both numbers by the same nonzero factor to keep the fraction's value. So 2/3 = 4/6.
Worked example
2/3 4/6 3/4 Two thirds and four sixths reach the same point. Three quarters reaches farther. Split each third into two equal pieces. The same shaded amount now fills 4 of 6 pieces. On a strip of the same length, 3/4 leaves only one quarter unshaded, while 2/3 leaves one third. The two amounts differ. If your child says… (8 concept checks in this chapter)
As you work through Fractions , listen for these everyday misunderstandings and use the prompt alongside each one.
If your child says…
“The triangle cannot be a half.”
Ask together Does each shaded section match the unshaded section when folded? What’s true The share's size relative to its whole matters, even when its shape changes. If your child says…
“Three inside ticks mean thirds.”
Ask together How many equal spaces do those three inside ticks make? What’s true The denominator counts equal spaces within a whole unit. If your child says…
“A fraction cannot be more than one.”
Ask together After making a whole roti, what remains on the plate? What’s true Counting fractional units can give an amount larger than a whole. If your child says…
“A smaller top number means the fraction is simplest.”
Ask together Can both numbers in two-quarters still be divided by 2? What’s true A fraction can simplify whenever a number greater than 1 divides both its numbers. If your child says…
“The bigger bottom number means more.”
Ask together Which reaches farther: the half-strip or the quarter-strip? What’s true The denominator alone cannot tell which fraction is larger. If your child says…
“I add the bottom numbers too.”
Ask together Did joining the pieces make each piece smaller? What’s true The denominator stays because the size of each fractional unit stays. If your child says…
“I can subtract different bottom numbers directly.”
Ask together How many quarter-sections does the half-piece cover? What’s true Express both amounts in matching fractional units before subtracting their counts. If your child says…
“The half and third already make a whole.”
Ask together What part remains unfilled if we use only the half and third? What’s true The half and third leave a gap that the sixth fills. Use this chapter three ways Previous chapter Perimeter and Area Next chapter Playing with Constructions
In the app, your child answers a short check-in with confidence taps, and you see which of these misunderstandings showed up—and which ones are gone.
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