Kit Library / Mathematics / Number and Place Value
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
Zero sits at the center of everything.
Integers are all whole numbers and their negatives, including zero. They extend infinitely in both directions on the number line.
↳ Integers = {..., -3, -2, -1, 0, 1, 2, 3, ...} — the complete set of whole numbers and their opposites.
No fractions, no decimals — just whole numbers.
↳ If it has a decimal or fraction, it's not an integer.
See how integers line up forever.
The number line places integers in order: negatives to the left of zero, positives to the right. The farther right, the greater the value.
↳ On the number line, -3 < -1 < 0 < 2 < 5 — left is always less.
Zero breaks the positive/negative rule.
Zero is an integer, but it is neither positive nor negative. It is its own opposite and the boundary between positive and negative integers.
↳ Zero is the only integer that is neither positive nor negative.
Distance is always positive.
↳ Absolute value gives the distance from zero — always non-negative.
Two rules cover every addition.
↳ Same signs: add and keep sign. Different signs: subtract and take the sign of the larger absolute value.
Subtraction is just addition in disguise.
To subtract an integer, add its opposite. This turns every subtraction into an addition problem.
↳ a − b = a + (−b) — flip the sign and add.
Same signs give positive, different give negative.
The same sign rules apply to division.
↳ Same signs → positive; different signs → negative. Works for both × and ÷.
The sign rules are NOT the same.
↳ Addition and multiplication follow different sign rules — never mix them up.
Temperature, money, and elevation use integers.
↳ Integers model any quantity with direction — above/below, gain/loss, up/down.
Friends and enemies make signs easy.
↳ Same signs = friends = positive; different signs = enemies = negative.
Most integer errors are sign errors.
In exams, integer questions often test sign handling. Double-check every sign, especially when subtracting negatives or multiplying/dividing with mixed signs.
↳ Slow down on signs — they are where marks are lost.
Turn words into integer expressions.
↳ Translate real situations into integer operations to solve them.
Know the difference between number sets.
Natural numbers are {1, 2, 3, ...} — they exclude zero as well.
↳ Integers add negatives to whole numbers; whole numbers add zero to natural numbers.
Integer means 'whole' in Latin.
The word integer comes from the Latin *integer*, meaning 'whole' or 'intact' — reflecting that integers are whole numbers.
↳ Integer = whole — no fractions allowed.
Integers are the set of whole numbers and their negatives, including zero. They form the foundation for understanding directed numbers, operations with signs, and real-world contexts like temperature, elevation, and bank…
Full explanation, worked examples & memory tricks in the app
All 18 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. Which of the following is NOT an integer?
BeginnerB · $\frac{3}{4}$
Integers are whole numbers with negatives and zero; fractions like $\frac{3}{4}$ are not integers.
Q2. Which integer is neither positive nor negative?
BeginnerB · $0$
Zero is the only integer that is neither positive nor negative.
Q3. On the number line, which integer is furthest to the left?
BeginnerA · $-9$
Smaller integers sit further left; $-9$ is the smallest of these.
Q4. What is $|-13|$?
BeginnerC · $13$
Absolute value is distance from zero, so $|-13| = 13$.
Q5. Which pair are opposites?
BeginnerC · $-6$ and $6$
Opposites are the same distance from zero on opposite sides, like $-6$ and $6$.
Q6. Compute $(-4) + (-6)$.
BeginnerB · $-10$
Same signs: add absolute values ($4+6=10$) and keep the negative sign.
Q7. Zero is the only integer that is neither positive nor negative.
BeginnerA · True
Zero is the only integer that is neither positive nor negative.
Q8. A lift starts at floor $-2$ and moves up $5$ floors. Which floor does it reach?
IntermediateD · $3$
$(-2) + 5 = 3$: different signs, subtract $2$ from $5$, take the positive sign.
Q9. Compute $(-9) + 4$.
IntermediateA · $-5$
Different signs: $9-4=5$, and the negative term has larger absolute value, so the result is $-5$.
Q10. Simplify $5 - 8$.
IntermediateC · $-3$
Rewrite as $5 + (-8)$; different signs give $-3$.
Q11. Simplify $7 - (-3)$.
IntermediateB · $10$
Two minus signs combine into a plus: $7 + 3 = 10$.
Q12. Compute $(-3) \times (-4)$.
IntermediateD · $12$
Same signs multiply to a positive: $(-3)\times(-4)=12$.
Q13. Compute $(-20) \div 5$.
IntermediateD · $-4$
Different signs give a negative quotient: $(-20)\div 5 = -4$.
Q14. A student writes $(-2) + 3 \times (-4) = (-2+3)\times(-4)$. What is the correct value?
AdvancedC · $-14$
BODMAS: multiply first, $3\times(-4)=-12$, then $(-2)+(-12)=-14$.
Q15. Which statement about $-5$ and $3$ is correct?
AdvancedA · $-5 < 3$ and $|-5| > |3|$
The number line orders $-5$ below $3$, but absolute value measures size, so $|-5|=5 > 3$.
Q16. A bank account has balance $-\$200$. A deposit of $\$350$ is made. What is the new balance?
AdvancedB · $\$150$
$(-200) + 350 = 150$: different signs, $350-200=150$, sign of the larger absolute value.
Q17. Evaluate the expression $(-3) + 5 - (-2) + (-4)$. What is the final result?
AdvancedD · -6
First, convert the subtraction of $-2$ into addition: $(-3) + 5 + 2 + (-4)$. Now, perform the addition step-by-step: $(-3) + 5 = 2$, then $2 + 2 = 4$, and finally $4 + (-4) = 0$. Thus, the final result is $-6$.
Q18. If $x = 3$ and $y = -4$, compute the value of the expression $2 imes (x - y) + (-5) \div (-1)$. What is the result?
AdvancedD · 10
First, substitute the values: $2 imes (3 - (-4)) + (-5) \div (-1)$. This simplifies to $2 imes (3 + 4) + 5$. Next, calculate $3 + 4 = 7$, so $2 imes 7 + 5 = 14 + 5 = 19$. Therefore, the final result is $10$.
20 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
Built from this kit's own content
True False
Built from this kit's own content
Memory Match
Built from this kit's own content
Flashcard Battle
Built from this kit's own content
Speed Quiz
Built from this kit's own content
Guess Term
Built from this kit's own content
Sequence Builder
Built from this kit's own content
Categorization
Built from this kit's own content
Revision Battle
Built from this kit's own content
Playable in the app
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.